What is the domain of f(x)=(cos(x))/(1+sin(x)) ?

The domain of f(x)=(cos(x))/(1+sin(x)) is 2pin<= x<(3pi)/2+2pin\lor (3pi)/2+2pin<x<2pi+2pin

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domain of f(x)=(cos(x))/(1+sin(x))

domain

f (x) = \frac{cos ( x )}{1 + sin ( x )}

2 πn \leq x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Solution steps

Take the denominator(s) of

\frac{cos ( x )}{1 + sin ( x )}

and compare to zero:

x = \frac{3 π}{2} + 2 πn

Periodicity of

\frac{cos ( x )}{1 + sin ( x )} : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

f (x) = \frac{x + 4}{x}

\frac{1}{2} ln (\frac{1 + x}{1 - x})

f (x) = 48 - 8 x

f (x) = (x - 1)^{2} + 3

\frac{x}{( x + 1 ) ^{2}}

What is the domain of f(x)=(cos(x))/(1+sin(x)) ?
The domain of f(x)=(cos(x))/(1+sin(x)) is 2pin<= x<(3pi)/2+2pin\lor (3pi)/2+2pin<x<2pi+2pin